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Test: Graphical Solutions - JEE MCQ


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20 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Graphical Solutions

Test: Graphical Solutions for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Graphical Solutions questions and answers have been prepared according to the JEE exam syllabus.The Test: Graphical Solutions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Graphical Solutions below.
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Test: Graphical Solutions - Question 1

Find the pairs of consecutive even positive integers both of which are smaller than 10 and their sum of more than 11

Detailed Solution for Test: Graphical Solutions - Question 1

Let x be the smaller of the two consecutive even positive integers .
Then the other integer is x+2.
Since both the integers are smaller than 10,x<10 ....(1)
Also the sum of the two integers is more than 11.
x+(x+2)>11
⇒ 2x+2>11
⇒ 2x>11−2
⇒ 2x>9
⇒ x>9/2
⇒ x>4.5....(2)
From (1) and (2) we obtain 4.5>x>11
Since x is an even number, x can take the values 6,8 and 10.
Thus the required possible pairs are (6,8).

Test: Graphical Solutions - Question 2

The solution to |3x – 1| + 1 < 3 is

Detailed Solution for Test: Graphical Solutions - Question 2

|3x - 1| + 1 < 3
|3x -1| < 2
Opening mod, we get
3x - 1 < 2,  -3x + 1 > 2
3x < 3,   -3x > 1
x < 1,   x > -1/3
-1/3 < x < 1

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Test: Graphical Solutions - Question 3

Which of the following is not a linear inequality?

Detailed Solution for Test: Graphical Solutions - Question 3
A is a quadratic equation not a linear equality because square of a function can't be negative
Test: Graphical Solutions - Question 4

For a student to qualify for a certain course, the average of his marks in the permitted 3 attempts must be more than 60. His first two attempts yielded only 45 and 62 marks respectively. What is the minimum score required in the third attempt to qualify?

Detailed Solution for Test: Graphical Solutions - Question 4

No of attempts = 3
Average =  (45+62+x)/3=60
x=73

Test: Graphical Solutions - Question 5

Which one of them is the solution for x, when x is integer and 12 x > 30?

Detailed Solution for Test: Graphical Solutions - Question 5

12x > 30
x > 30/12
x > 2.5
x is an integer. So, minimum value of x is 3.

Test: Graphical Solutions - Question 6

Find the value of x which satisfies 5x – 3 < 7, where x is a natural number.

Test: Graphical Solutions - Question 7

If -5x+2<7x -4, then x is

Detailed Solution for Test: Graphical Solutions - Question 7

 -5x + 2 < 7x - 4
6 < 12x
x > 1/2

Test: Graphical Solutions - Question 8

The solution to 5x-3<3x+1, when x is an integer, is

Detailed Solution for Test: Graphical Solutions - Question 8

We have 5x−3<3x+1
⇒5x−3+3<3x+1+3
⇒5x<3x+4
⇒5x−3×<3x+4−3x
⇒2x<4⇒x<2
When x is an integer the solutions of the given inequality are {.............,−4,−3,−2,−1,0,1}
Hence {x / xεZ, x<2}

Test: Graphical Solutions - Question 9

The inequations -4x+1≥0 and 3-4x<0 have the common solutions given by

Detailed Solution for Test: Graphical Solutions - Question 9

-4x+1≥0 and 3-4x<0

 1 ≥ 4x and 3 < 4x

1/4 ≥ x  and 3/4 < x

so x ∈ (-∞,1/4] U (3/4 , ∞ )

Test: Graphical Solutions - Question 10

Solve the following linear inequality for x: 12109_image003

Detailed Solution for Test: Graphical Solutions - Question 10

(2-3x)/5 ≤ (-x-6)/2
By cross multiply we get
4-6x ≤ -5x-30
-x ≤ -34
x ≥ 34

Test: Graphical Solutions - Question 11

A point P lies in the solution region of 3x – 7 > x + 3. So the possible coordinates of P are

Test: Graphical Solutions - Question 12

A connected planar graph having 6 vertices, 7 edges contains _____________ regions.

Detailed Solution for Test: Graphical Solutions - Question 12

By euler’s formula the relation between vertices(n), edges(q) and regions(r) is given by n-q+r=2.

Test: Graphical Solutions - Question 13

If 5x+6<2x-3, then

Detailed Solution for Test: Graphical Solutions - Question 13

5x+6<2x-3
5x-2x < -3-6
3x < -9
x<-3

Test: Graphical Solutions - Question 14

The region x > -3 lies

Test: Graphical Solutions - Question 15

If a < b then -a ______ - b

Test: Graphical Solutions - Question 16

The solution of inequality 4x + 3 < 5x + 7 when x is a real number is

Detailed Solution for Test: Graphical Solutions - Question 16

4x+3<5x+7
4x+3−7<5x+7−7
4x−4<5x
4x−4−4x<5x−4x
−4<x
Thus, the solution set of the given inequality is (−4,∞).

Test: Graphical Solutions - Question 17

Two less than 5 times a number is greater than the third multiple of the number. So the number must be

Test: Graphical Solutions - Question 18

What values of x satisfy -6x>24 and x is an integer?

Detailed Solution for Test: Graphical Solutions - Question 18

- 6x < 24
=> 6x < -24
x < - 4

Test: Graphical Solutions - Question 19

The solution set of 4580_image005, where x is a real

Detailed Solution for Test: Graphical Solutions - Question 19

X/3-x/2 > 1
-x/6 > 1
x/6 
x < -6
therefore x belongs to the range (-∞,-6)

Test: Graphical Solutions - Question 20

Find the value of x when x is a natural number and 24x< 100.

Detailed Solution for Test: Graphical Solutions - Question 20

24x < 100
⇒ x < 100/24
⇒ x < 25/6
 It is evident that 1,2,3 and 4 are the only natural numbers less than 25/6,
Thus  when x is a natural number ,the solutions of the given inequality are 1,2,3 and 4.
Hence, in this case, the solution set is {1,2,3,4}.

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